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The Best %*@$#?^” Regents Physics Review Sheet Ever!Math, Graphs, and Vectors:1. The fundamental SI Regents Physics units spell “MASK”: meters, amperes, seconds and kilograms All other units are derived. In calculations, leave original units if not sure. ”” means “final – initial”2. W = work (energy) or watts. w = weight. m = mass or meters. P = power, but p = momentum. J = impulse or joules. E = energy or electric field. T = tension or period. Time t must be in seconds! 3. Recognize quantities by units: distance d (in m), speed v (in m/s), acceleration a (in m/s2), mass m (in kg), force F(in N), etc. Quantities with no units: coefficient of friction and refractive index n Use equation to determine units. Ex: units for [Work] = [F][d] = [ma][d] = kg·m/s2·m = kgm2/s2 = 1 J4. Unless the answer is prefixed, get rid of prefixes, eg, the c in cm (except the k in kg) before a calculation. 5. Scalars have magnitude (size) only. Ex: distance, mass, time, speed, coefficient of friction, all energies, work, power, charge, resistance, potential difference, , T, f, , , refractive index6. Vectors = scalar (magnitude) + direction. Ex: displacement, velocity, acceleration, all forces, all fields, momentum, impulse, etc. Vector = arrow. Draw with ruler to scale. Draw the arrow tip!7. Add vectors A and B using either: a/ tip-to-tail: Resultant from tail b/ parallelogram: of A to tip of B Resultant is diagonal.

8. Magnitude of R depends on angle between the two vectors being added. See diagram 1.At 00: mag. of R = A + B. At 1800: mag. of R = A - B. At 900, mag. of R = √(A2 + B2). From the sum (max.) to the difference (min.) is the total range of possible resultant magnitudes.

9. Any vector can be resolved (broken down) into an infinite number of paired components.10. “Show your work” means: equation, substitution with units, answer with units11. Plot points. If a straight line, use a ruler. Use best-fit line (not data points) to calculate slope. Find what slope represents by forming ratio: y-quantity/x-quantity, then look in PhysRT. Ex: Plot a vs. F. What does slope represent? a/F =? See PhysRT, where a/F = mass m

Kinematics (Study of Motion):12. distance d = position. DVD ~ 10-3 m thick, your finger ~ 10-2 m wide, and DVD ~ 10-1 m wide displacement d (vector) = distance (scalar) + direction. Distance is the magnitude of the displacement.13. speed v = the rate of change in distance. Average v = d/t. Speed is the magnitude of the velocity. velocity v = rate of change in displacement velocity v (a vector) = speed (a scalar) + direction 14. Add v’s as vectors: resultant vplane w.r.t. ground = vplane w.r.t. air + vair w.r.t. ground15. acceleration a = time rate of change in velocity. a is a vector. a has same direction as v.16. a/ The slope of the distance-time graph = speed. Greater speed greater slope. b/ The slope of the velocity-time graph = acceleration. Greater acceleration greater slope.

c/ The area under the velocity-time graph = displacement. Positive area positive d (right or up).17. Uniform motion = constant velocity a = 0

Pattern: Graphs:

18. Accelerated motion = constantly changing velocity acceleration = constant for Regents PhysicsPattern: Graphs:

19. Word clues: Starts from rest: vi = 0; comes to rest: vf = 0; average vavg = (vi + vf)/2 (not in PhysRT) Use vavg for v in d = vt. Positive is up or right, negative is down or left. 20. If a and v are same direction, speed is increasing. If a and v are opposite direction, speed is decreasing.21. Free fall (no air resistance): a = -g = -9.81 m/s2 (independent of mass and speed). 22. For a dropped object: vi = 0, d = -4.9t2 and vf = -9.8t. Falls d = -4.9 m in 1st second (NOT -9.8!)23. Projectile fired straight up: Remember the symmetry between times and speeds going up and down.

speeds vup = vdown, tup = tdown = ½ ttotal, vtop = 0, BUT atop = -9.81 m/s2. It is still in free fall!24. Horiz. fired project.: vi is horiz.: vi = vix = const., viy= 0, and vy = -gt. a = ay = -9.8 m/s2. See diagram 4. Rate of fall is indep. of vi and same as for dropped object. Dropped and fired hit at same time! Parabolic trajectory. Velocity v tangent to path. Fnet = weight = downwards, so is a. Fx and ax = 0.

25. Projectile fired at angle with initial speed vi: Symmetry as in straight-up case. See diagram 4.Velocity is tangent to path. Fx and ax = 0. Fnet = Fg = weight downward, so a is also. Still free fall.Horiz. comp.: vix=vicos stays same. Use TOTAL time to find range: dx = vix x ttotal

Vert. comp. viy=visin, Use viy as initial speed and solve problem as a ball thrown straight up Speeds vup = vdown, tup = tdown = ½ ttotal, BUT vtop = vix and is ≠ 0. As before, atop = -9.81 m/s2

Trajectory is parabolic. With air resistance, range and max. height are less and no longer parabolic Max. range if = 450. Max. height and max. time if = 900. Complementary angles (eg, 200 & 700) have the same range, but higher angles have longer ttotal and reach a higher max. height.

Forces, mass, Newton’s Laws and Gravity:26. A force F is a push or pull. Forces are vectors: F = magnitude (strength of force) + direction.27. Forces measured in newtons, N (derived). 1 N = 1 kg·m/s2 = weight of a stick of butter or small apple28. Two basic types: a/ contact: normal, tension, friction. b/ at a distance: weight & other field forces29. Isolate all forces with a free-body diagram. Draw only forces (no v, p, etc) acting on the object. Resultant force depends on angle between vectors: Add if 00, Subtract if 1800, etc, as in #7-8 above. Resolve into x- and y-components with: Fx = Fcos and Fy = Fsin. See diagram 5.30. All mass has the property (not a force) inertia = resistance to velocity. More mass more inertia. Convert masses to kg before any calculations! 1$ bill ~ 10-3 kg, butter or apple ~ 10-1 kg, student ~ 50 kg31. Newton’s 1st: No net force needed for motion. Otherwise known as the Law of Inertia:

“An object at rest tends to stay at rest, and an object in motion tends to stay in motion.”In other words: Net force = 0 object is in equilibrium a = 0 constant velocityIn equilibrium: up and down (y) forces balance, right and left (x) forces balance. See diagram 5.

If forces are balanced (Fnet = 0), object may be at rest OR moving with constant velocity.32. Equilibrant force (-R) is equal in magnitude but opposite to the resultant vector (R). See diagram 2.33. Newton’s 2nd: a = Fnet/m. Rearrange: Fnet = ma. a has same direction as the net F. A net, unbalanced force (object not in equilibrium) MUST produce acceleration. F’s cause a’s. To find a: Find net F by adding force vectors. Divide by mass (not by the weight!). 34. Elevator: Accelerating up FN (what scale shows) increases; accelerating down FN decreases 35. Newton’s 3rd: A exerts force F on B. B exerts force –F on A. These equal and opposite forces always are same type, but act on different objects. Forces, NOT the accelerations, must have equal magnitude.Note: If F1 = your weight of 600 N. Then reaction to F1 = You pull up on Earth with a 600-N gravity force. 36. Gravity and Weight: All masses attract each other with a gravitational force Fg (weakest force) Fg = Gm1m2/r2 Ex: 2r ¼ F, 3r 1/9 F, etc, 2m 2F, 3m3F, 2m AND 2r F/2, etc (inverse square) Stronger as you move closer: (1/2)r 4F, (1/3)r 9F, etc37. G = universal gravitational constant is NOT the same as g = the acceleration due to gravity.38. Weight (in N) w = mg = Fg = force of Earth’s gravity acting on object. If g ≈ 10 m/s2, then w ≈ 10mass.39. A gravitational field g exists around every mass. g is radial and inward for a point mass. See diagram 7.40. g = Fg/m = strength of gravitational field (in N/kg) = acceleration a due to gravity (in m/s2) = w/m g is proportional to 1/r2, so weight = mg is also 1/r2. Note: 2RE above surface is tripling the distance! On or near the surface of a planet, g is constant as long as you don’t get too far away. See diagram 7. 41. Mass m is same everywhere. Weight w changes, b/c g changes: w = mg. Eg, gMoon = (1/6)gEarth

Uniform Circular Motion, Momentum, Impulse, Friction:42. Centripetal forces Fc can be provided by a string, road friction, a seat, air, etc. In absence of centripetal force, objects fly off on a tangent to the circle (NOT directly away from the center of the circle). 43. Centripetal Fc (a net force and ≠ 0) and ac are directed toward the center of the circle. See diagram 8.44. Velocity vector is tangent to the circle, but changes direction, so it accelerates alhough speed is constant. 45. Both ac and Fc are directly prop. to v2, and inversely prop. to r. Fc (NOT ac!) is directly prop. to m. 46. Momentum p = mv is a vector in same dir. as v. Objects can have inertia (mass), but no p if v = 0.47. Changes in p: p = mvf – mvi = m(vf – vi) = mv. Elastic (hit & bounce) collisions greater p 48. Impulse J = Fnett = p same units: 1 N·s = 1 kg·m/s (but ≠ newton). J is a vector w/same dir. as Fnet In plot of F vs. t, area = J. Impulse Fnett = p Maximize p by increasing F or t (follow through)49. Momentum is conserved in all isolated (from friction) systems. For collisions/explosions, use:

(before) m1v1 + m2v2 + … = m1v1' + m2v2' + … (after) (v’s can be negative!)

If objects start from rest, both left-hand v’s = 0. Ex: Spring between masses is released.If objects collide and come to rest, the right-hand v’s = 0. Hit and stick (inelastic) collisions: Both m’s have the same final speed v1' = v2' = v'

50. Friction Ff is a force usually opposite to v. It converts KE into internal (heat) energy. 51. Ff depends on 1/ the nature of the two surfaces (see table of ’s) and 2/ the normal force, FN: Ff = FN. Sliding friction is roughly independent of surface area and speed. 52. Kinetic friction is < maximum static friction. (It takes more force to start it moving .)53. Coefficient of friction has different values for object at rest (static s) or moving (kinetic k).54. Normal force FN = weight = mg (NOT mass alone) for horizontal flat surfaces with no extra forces. 55. Inclined plane: Components of weight w: wperp = wcos and wll = wsin. See diagram 3. Increasing increases wll and decreases wperp but does not change w itself. 56. In equilibrium, wperp = FN and wll = Ff or any other force(s) holding object up the incline. If no friction, Fnet = wll, and object accelerates down incline at a rate: a = gsin.

Energy: 57. W = Fd. This is true only for component of F in dir. of motion. No W if d = 0 or if F perp. to d. Work = area under the F (y-axis) vs. displacement (which can be d, h, or x) graph. See diagram 6.58. Power P is the rate at which energy is converted from one form to another. Like W, P is a scalar. Units of P: watts, W. “Watt? Don’t worry, joule get it in a second!” 1 W = 1 J/s 1 J = 1W·s59. Potential energy PE is stored in system, eg, chemical, gravity, spring, in E or B fields. Units: joules, J60. Gravitational PE = work done in lifting an object to a height h above a reference level. Path does not matter, only h. PE = mgh is directly proportional to m, g and height raised h. 61. Hooke’s Law: For ideal spring, stretch (compression) x is proportional to the applied force: Fs = kx62. Spring constant k is the slope of F(y axis) vs. x plot. Stiffer spring steeper slope bigger k63. Elastic PEs = ½kx2 equals work done in stretching or compressing a spring = area under F-x graph64. Kinetic energy is proportional to m and v2: KE = (1/2)mv2 = work done to accelerate a mass65. Work done on system increases its energy W = Fd =ET = KE + PE + Q (internal E). Work & ALL energies have same units: joules: 1 J = 1 N·m = kg∙m/s2 ∙m = kg∙m2/s2 = raise apple 1 m Work can change each of these separately depending on how it is done:

a/ On a horizontal surface: W = Fd = KE = ½mv2 (Work changing v)b/ At constant speed: W = Fd = PE = mgh or ½ kx2 (Work stored PE)

c/ On a surface with friction: W = Fd = internal energy (Work heat)66. Mechanical energy is the sum of the potential and kinetic energy of an object: Emech = PE + KE67. Law of Conservation of Energy. See diagram 9. In a system isolated from friction (Q = 0), energy can be converted from one form to another but not destroyed! ET = constant:

(before) PE + KE = PE' + KE' (after)

If there is friction, total “after” mech. energy (PE' + KE') is less b/c energy is converted to heat (internal E)68. ET does not change for a free falling mass, a swinging pendulum, or a mass compressing a spring (Ignore friction). KE PE. If KE decreases, PE increases by same amount, and vice versa. Ex: Free fall a height h from rest or pendulum, PE becomes KE: mgh = (1/2)mv2. Solve for v=√(2gh)

Static Electricity:69. Charge q on an electron or proton = 1 elementary charge = e = 1.60 x 10-19 C. Not always stated! Milliken’s oil drop experiment found q on electron was the smallest possible (a quantum). 70. Removing electrons (e-, not e) from an object makes it more positive; adding them makes it more neg. Net charge is the excess. It can be measure in e's or in coulombs, C. 1 C = 6.25 x 1018 e.71. Like q's repel, opposite q's attract. The closer the charges, the stronger the electrical force. If object A is attracted to a charged object B, A could be neutral or charged oppositely to B. If object A is repelled by a charged object B, A must have the same charge as B.72. Charge is conserved. The sum of charges before = the sum of charges after. Always.

(before) q1 + q2 + … = q1' + q2' + … (after) Signs matter!

3 A2 A

1 or 5 A

73. One’s objects loss in charge = other object’s gain. Ways to charge objects (see diagram 11): a/ Friction: rub two insulators charges are directly moved from one object to other b/ Contact: Two metals touch excess charge is spread out over both metals b/c charges repel In metals: e-'s can move, so excess e-'s repel and spread themselves out on outside surface. Ex: If 2 identical metal spheres touch, divide TOTAL charge by 2 to find q on each. c/ Induction: Bring “+” object near neutral conductor, ground opposite side, conductor becomes “-“74. Coulomb’s Law: Every two q’s exert an electric force Fe on each other: Fe = kq1q2/r2 (inverse square) Ex: 2r ¼ F, 3r 1/9 F, etc, 2q 2F, 3q3F, 2q and 2r F/2, etc

As you move charges closer, F increases: (1/2)r 4F, (1/3)r 9F, etc75. An electric field E = Fe/q exists around every charge q. See diagram 10. Units: [E] = [Fe]/[q] = N/C. 76. E is a vector with direction given by the direction of the electric force Fe on positive test charge q. 77. E = 0 inside a conductor, even if there is charge q on conductor. Safe in a metal car hit by lightning.78. E field lines: Lines of electric F; closer lines stronger E; lines don’t cross; Fe is tangent to lines 79. E field of 1 charge is radial and 1/r2. Lines are out of a positive q, but into a negative q E fields of 2 charges is similar to the B field around two magnets. See diagram 10.80. E field of 2 parallel plates: constant, equally spaced lines except near edges, out of + and into – plate Fe on q between plates has same mag. and dir. everywhere because Fe = qE, and E is constant. Proton between plates feels same mag. Fe as electron, but opposite dir. Proton a is less b/c more m. 81. Potential difference V = W (work or energy)/q = energy needed to move a charge q in a E field. Units are volts, V. If W in J, then q in C. If W in eV, then q in e. 1 V = 1 J/C = 1 eV/e An electronvolt eV is a tiny energy (NOT a voltage) unit. To convert: 1 eV = 1.60 x 10-19 J.

Current and Circuits:82. Current I is the rate of charge q passing a point. Need a complete circuit and potential difference. Conservation of charge at a node (junction): Iin =Iout.

83. I = q/t Charge q in coulombs, C, I is in amperes, A. If q is given in electrons, convert to C first. 84. Potential difference (voltage) sources: batteries (DC), generators (AC), etc, all supply energy85. Electrons e- move most easily. Conventional I is positive and moves from high to low potential.86. Electron collisions make drift velocity slow compared to actual e- speed between collisions.87. Conductors (metals, ionized gases, etc) have e- free to move. Insulators: e- and free and hard to remove.88. Resistivity values given in PhysRT are used to calculate R for metals. Smaller smaller R. Units: Ohm·meters: ·m. In the equation with , area A = r2 with r in meters for wires. 89. R = L/A Short, thick, cold silver wires make the best conductors. 90. Ohm's Law: Resistance R = V/I = slope of V (y-axis) vs. I graph. Units: ohms 1 = 1 V/A If graph of V vs. I is straight ohmic. True for most metals at constant temperatures. 91. For given voltage: If no R short circuit (danger). Higher R less I. If R = ∞, I = 0 open circuit.92. Voltage represents energy used to push electrons around. Assume no voltage loss along circuit wires. Voltage is “across” two points, but current is the charge passing “through” circuit element.93. Series circuits: More resistors more total R less I less power P. (see PhysRT V divides up in direct proportion to the R of each part. for equations) I is the same in all parts of circuit, UNLESS you change the circuit!!!! See diagram 12. Disconnecting one part of series circuit makes I = 0 in the entire circuit.94. Parallel circuits: More resistors LESS total R more I more P faster power drain (see PhysRT Current divides up in inverse proportion to the R of each part. for equations) V is the same across all branches of the circuit. See diagram 12. If one parallel element is disconnected, rest of circuit is NOT affected.95. Series resistors: Req = sum = bigger than biggest R. For n equal series resistors R: Req = nR Parallel resistors: Req = smaller than smallest R. For n equal parallel resistors R: Req = R/n96. Voltmeters are hooked up across (in parallel). Ammeters are hooked up in series. See diagram 12.97. Electrical energy W and power P: Add W or P for each part of circuit, regardless of series or parallel.Magnetism and Electromagnetism (E&M): 98. Magnetism is caused by current I. A magnetic field B exists around every I (any moving q). 99. Direction of a magnetic field (B) = the direction that the N pole of a compass points.

100. B field lines point from the N pole to the S pole outside the magnet and from S to N inside the magnet. 101. In iron, nickel and cobalt, magnet domains are lined up. This can be randomized by raising temperature.102. B field of bar magnet: Lines out of N, into S pole. Denser lines stronger field. Lines don’t cross. B force is tangent to the B field lines. Strongest near poles. Every N has a S pole (no monopoles). 103. Like poles repel, opposite poles attract. Know the B Field of two bar magnets. See diagram 13.104. Earth’s B field is like a bar magnet, drifts and flips occasionally, and is a S pole near geographic North. 105. Solenoid (coil) B is like a bar magnet and stronger with more I or more wire turns or adding an Fe core. 106. Electromagnetic induction: Relative motion v betw. conductor and B field induces voltage in conductor. Either conductor or magnet can move. Max. voltage V if angle between v and B is 900, minimum if 00. 107. Motors and generators both use the force that a B field exerts on moving charges: same hardware. motors: electrical energy to mechanical generators: mechanical energy to electrical.

Vibrations and Waves:108. Period T = time to complete one cycle = time for a wave to travel one wavelength.109. Frequency f = number of vibrations or waves per second. 1 Hertz hz = 1/s = s-1 = 1 cycle per second.110. T = 1/f T is the inverse of f and vice versa. Period T must be in seconds.111. Amplitude A = displacement from equilibrium (half of peak-to-peak value). See diagram 14.112. Simple (small A) pendulum: T increases (and f dec.) with length, independent of bob mass and A113. Resonance occurs when an object is forced to vibrate at its natural frequency. The result is an increase in the A (NOT the f!) of vibration. Ex: bridges, wine glasses, air in tubes, strings, swings, etc114. Vibrations cause pulses and waves. A pulse = single disturbance of medium. Repeated pulse = wave. A wave is a periodic disturbance of a medium that transports energy, but NOT mass. 115. medium (pl. media) is what a pulse or wave propagates through: vacuum, gases, water, solids, liquids, etc116. wavelength = distance d between successive identical points on a wave = d that wave travels in 1 T117. phase: how much a wave is shifted relative to reference point or another wave phase angles: 1 = 3600, ¾ = 2700, ½ = 1800, ¼ = 900

118. Longitudinal: wave v and medium v are parallel. Transverse: wave v perpendicular to medium v 119. For transverse waves: Leading edge points move up, trailing edge points move down. See diagram 14.120. Wave v depends on properties of medium (for example temperature, density, etc), not on amplitude Wave speed v = d/t or v= f. Units: m/s = Hz·m. 121. If v remains constant, increasing f decreases and vice versa.122. Interference: Two or more waves in same medium at same time. Interference is a wave property. Superposition: Add 2 or more waves algebraically to get a resultant wave. See diagram 15.123. Constructive interference Resultant amplitude is greater. Sounds louder or appears brighter. Waves are in phase. Phase difference = 0, 1, 2, … or 00, 3600, 7200, …124. Destructive interference Resultant amplitude is less. Sounds quieter or appears dimmer. Waves are out of phase. Phase difference = ½, (3/2), (5/2), … or 1800, 5400, 9000, … Total destructive interference: Waves have equal amplitudes and are completely out of phase. Resultant is zero. Sound (noise) or light cancels out completely. 125. Standing waves: interference of two waves with same A, speed and f, but opposite directions. Nodes = no movement, destructive interference. Antinodes = constructive interference. See diagram 16.126. Diffraction = bending of wave behind an obstacle or opening. Diffraction inc. as inc. or as size d of opening or obstacle dec. Diffraction is a wave property. Same and v behind obstacle. See diagram 19.127. Double-slit experiment combines diffraction and interference from 2 waves. See diagram 15.128. Doppler effect: Change in observed f of wave due to relative motion between source S and observer O

If S and O are approaching: higher f (higher pitch or bluer light) and shorter Same v for both.If S and O are receding: lower f (lower pitch or redder light) and longer Same v for both.The source f remains constant! The faster the relative motion, the more the f. See diagram 17.If relative motion is at constant v, f remains constant. If motion accelerated, f will change.

Sound vs. Light waves:129. Sound waves are longitudinal, mechanical waves that need a medium. Sound does not travel in a vacuum. The amplitude A = loudness (energy), and frequency = pitch (bass or treble to ultrasound). 130. When charged particles are accelerated, electric E and magnetic B fields are induced. The fields are

fE

mE

Eph = hfslope = h

E Eph = hc/ h = Planck’s constant

slope = c2

perpendicular to each other and to the wave velocity. This electromagnetic (E&M) radiation travels at v = c (3.00 x 108 m/s) in a vacuum. c is the maximum speed limit for any object in the universe.131. Visible light and the E&M spectrum (radio, microwave, IR, UV, x-ray, gamma rays) are transverse. 132. Wave model of light: Amplitude A = energy = brightness, but frequency f = color (visible light).133. Light is about a million times faster than sound. See the PhysRT page 1 for actual speeds. Sound v increases as density of medium increases, but light v decreases with increasing density.

Reflection (valid for all waves, but mostly applied to light). See diagram 20. 134. At any boundary between 2 media, light can be a/ reflected back into original medium, b/ refracted (bent) into the second medium, or c/ absorbed (increases internal energy).135. All angles in wave problems are measured with respect to the normal and in degrees!136. Law of Reflection: i = r Incident and reflected waves have same v, and f (color)137. A corner reflector returns the ray parallel to the incident ray.138. Images in plane mirror are ALWAYS the same size as object and same distance away as object is!139. Regular (specular, mirror) reflection occurs at smooth surfaces. Diffuse reflection at rough surfaces. Law of reflection is obeyed in diffuse reflection, but normals are not parallel, so light is scattered.

Refraction and Snell’s Law. All angles in degrees. Degrees are units! See diagrams 21 and 22. 140. Absolute index of refraction n = c/v (no units). Snell’s: n1sin1=n2sin2. n2/n1 = v1/v2=1/2

141. Bigger n slower speed v. In new medium f (color) and T of light remain the same. Since v changes but f constant, changes. Relative index n2/n1 factor by which v slows and decreases 142. Refraction is the bending of light (or any wave) that occurs as it enters another medium. To refract, it must enter a/ obliquely (at an angle other than 00) and b/ change speed. Bigger n more bending143. Decrease angle (towards normal), decrease speed. Increase angle (away from normal), increase speed. 144. For a rectangular prism, light leaving the prism is parallel to the ray entering the prism, but shifted.145. Total internal reflection: Only for slow to fast v change. At critical angle, wave is refracted at 900. 146. Dispersion is the separation (splitting up) of white light into its different frequencies (colors). A prism or raindrop produces a rainbow because blue slows more, so it bends more than red (nblue > nred). See diagram 18.

Modern Physics: See diagrams 23. 147. A quantum is the smallest possible particle of something. Ex: a photon (particle of light) or the e- charge148. Duality: Light can act like a wave (interferes or diffracts) or a particle (photoelectric effect or collisions). 149. A photon is a particle of light with energy (no mass!) directly proportional to its frequency f and inversely proportional to its wavelength . Convert E in eV to joules before calculating f or !!!

Bright light more photons than dim light. Blue light higher f (more energy) than red light. Photoelectric Effect: Photons kick e-'s out of metal only if photon f big enough. UV works, but not red.150. Duality: Matter can act like a wave (diffracts or interferes, used in an e- microscope) or a particle.151. Rutherford discovered tiny “+” nucleus by firing alpha particles at gold-foil: A few bounced back!152. Bohr model: “solar system” with discrete e- orbits around positive nucleus: Energies are quantized.

Photon absorbed e- moves up. Subtract e- energy levels (ignore negative signs) to get Eph

Photon emitted e- moves down. Subtract e- energy levels (ignore negative signs) to get Eph

Photon energy MUST match energy of e- exactly, except during ionization (see next line).Energy needed to remove e- = ionization potential (any extra energy goes into the KE of e-)For hydrogen: transitions to n = 2 visible lines (each line represents one e- transition)

transitions to n = 1 more Eph higher f of light UV lines transitions to n = 3 smaller Eph lower f of light IR lines

One e- transition can produce multiple photons. Ex: n = 3 to n = 1 3 photons: 31, 32 and 21Problems w/ Bohr: e- accelerates, radiates, spirals in, should be a continuous spectrum, but was discrete!153. Energy can be converted to mass and vice versa: Use E = mc2 (mass is kg) OR 1u = 931 MeV. More mass means more energy. Slope of E vs. m equals c2. c2 is simply a conversion factor, and does not imply motion.

F1

F2

R

-R = equilibrant

Fnet = w

ax=0ay = -g

5. Forces:

Fx = Fcos

Fy = Fsin

F

Fnet = 0 a = 0at rest OR const. v

Fnet ≠ 0 a to rightvel. can bepos. or neg.

fired witha certain vi

fired with a speed 2vi

900

R =diagonal

1800

R = difference = minimum

vtop ≠ 0

F

w = FN w = T

FN

00

R = sum = maximum

w

wperp = wcos

wll = wsin

At rest:

154. 1 universal mass unit u = (1/12) mass of C-12 nucleus. Masses can be given in u or in kilograms.155. In fission or fusion, “missing mass” is converted into energy (E = mc2)

reactant 1 + reactant 2 + …. product 1 + product 2 + … + ENERGY

Add up reactants, add up products, then subtract represents energy released (aka “mass defect”)156. Matter-antimatter annihilation: mass + antimass 2 photons. Each photon Eph = (mass)c2

Pair production: 1 photon mass + antimass. The photon Eph must be at least = 2(mass)c2

157. Total mass-energy is conserved, but mass and energy by themselves are NOT, b/c m E158. Only charged particles can be accelerated in a particle accelerator. Energy gained is W = qV.159. Only integer multiples of e = 1.60 x 10-19 C can be found on any particle. (Except quarks.)160. Quarks: charge = (+2/3)e or (-1/3)e, with opposite charges for antiquarks.161. Matter m with charge q has antimatter with same mass m but opposite charge –q. See diagram 24.162. All matter is either a/ a lepton or b/ a hadron. Hadrons are either: a/ mesons (qq) or b/ baryons (qqq). Quarks are never found alone. That is why it is ok that they have charge that is a fraction of e. Add up charge on all quarks in particle to find total charge on particle, which must be an integer.163. The antiparticle of a meson qq is qq. The antiparticle of a baryon qqq is qqq. Same m, but opposite q.164. Protons (uud) and neutrons (udd) are made of up and down quarks because those two quark flavors

are the most common and the least massive flavors. More massive quarks are formed at higher energies.165. The 4 Fundamental Forces (excluding dark energy):

1. Strong nuclear (strongest) always attractive and very short range holds the nucleus together Protons are attracted to other protons (and to neutrons) if close enough by this force!

2. Electromagnetic between q’s attractive OR repulsive, 1/r2, and infinite range3. Weak nuclear important during radioactive decay (don’t need to know for Regents Physics)4. Gravity (weakest) always attractive, 1/r2, and infinite range. Important b/c planets are neutral.

Diagrams:1. R depends on direction between vectors:

2. Equilibrant: 3. Inclined plane:

4. Projectile Motion: In both cases: parabolic trajectories and F and a are down!

dropped ball

string

FN = w + F

CWv

F, a

v

v

F, a

F, a

F, aCCW

F, a

v

vF, a

vF, a

v

F, a

ET = PE + KE = constant Loss of KE gain of PELoss of PE gain of KE

PE

KE

ETE

b/ by induction:

positive charge

negatively chargedobject:

a/ by contact:

neutralconductor Touching – equal q on each.

(If 1 sphere bigger more q)separate

neutralconductor:chargesseparate ground

Remove ground, then remove thecharged object.Note: charges nowopposite originalcharged object.

chargedobject

chargedconductor

g ~ 1/r2 for apoint mass:

Earthw

Fg (weight) or g as a function of distance from Earth:

1Re 2Re

1Re 2Re 3Re 4Re

3Re 4Re

5Re from center

w4

w9

w16

w25

from surface

A

Series: I sameV = V1 + V2

Parallel: V same I = I1 + I2

A

9. Conservation of Energy for a freely falling object or a pendulum with no friction:

AA

dF

W = Fd

6. Work:

d

W = Fxd = Fcosd

F

V V V

slightlycurvedat edges

d

F

W = 0b/c = 900

d

FW = Fd

g = 9.81 m/s2 is constant at Earth’ssurface:

7. Gravitational fields g:

8. Uniform circular motion:

10. Electric fields:

11. Charging (all diagrams could have all charge signs reversed):

12. Circuits:

A

VV

V

A

V across anywhere, but A in series with different elements.A in series anywhere, but V across different elements.

Sbreak magnet:

Transverse wavevelocity to right:

Transverse wavevelocity to left:

Up and down arrows arevelocity of medium.Troughs and leading edgesare always moving up.Peaks and trailing edges are always moving down.

2-slit diffraction and interference:

L:

higher f (blue)shorter same v

lower f (red)longer same v

source v

around an obstacle:

around acorner:

Bigger or smaller d: More diffraction

18. Dispersion:

glassprism

whitered

violet

rain drop:

pulse

NP of compass= direction of B

constructive: destructive: completedestructive:

Through anopening: always

same ason other sideof barrier

16. Standing WavesL L = 3 :

2

L

d

A

BC

DE

FG

H

IIn phase (1): AE, BF, CG, DH, EI, and AI (2)Completely out of phase (1/2 ): AC, BD, CE, DF, EG, FH, GI. Also (3/2 ): AG, BH, CI

Awave:

compressions rarefactions

= destr. = 0, ½ , 3/2 , …

= constr. = 0, 1, 2, …

L = : 2

L

13. Magnetic fields around magnets and a broken magnet:

14. Pulses and waves

15. Interference:

17. Doppler Effect:

19. Diffraction:

N

SN S N

Smaller or bigger d: Less diffraction

redviolet

Before:

e- atrest

photonat v = c

e- now has KE

Eph is less, so longer, but v still = c

22. Refraction of Light:

wavefronts:

incident waveswith v1, f1, A1(reflected wavenot shown)

transmitted waveswith v2, f2, A2

faster

slower

smaller n

bigger n

If rays 1 and 2 are parallel, then n1 = n2 (same v)

slowest

1

2

1

2

fastest

fastest

slowest

samesame

fastest

Bigger angle, faster v, and vice versa. Same angle, same v:

wave-fronts: rays:

Images in a flat mirror m:Same sizeSame distance

i = r

m

boundary

v1 v2

n1 n2

meson:

s u

hadrons & leptons (which occur by themselves)

baryon:

u du

Some of photon E and momentum are transferred to e-.ET and pT are conserved e- gains what photon loses

uud = (+2/3)e + (+2/3)e + (-1/3)e = +1e (a proton)

24. Standard model: All matter is made of…

su = (-1/3)e + (-2/3)e = -1e

The antiparticles are: uud = -1e and su = +1eThey have the same mass as their antimatter.

i r

o ispecular:

diffuse:

20. Reflection:

21. Wavefronts entering a new medium in which its speed is slower v1 > v2 (a wave traffic jam):

Compare: v1 > v2 (given), n2 > n1, A1 > A2 (some reflected), 1 > 2, but f1= f2 (same frequency!)

23. Photon-electron collisions (Compton Effect) Light acting like a particle:

After: